James Milner believes winning the Capital One Cup would hasten Liverpool’s transition under Jürgen Klopp and insists the team should be proud to be competing on four fronts despite their indifferent form.

Liverpool reached a 12th League Cup final with a penalty shootout victory over Stoke City on Tuesday to give Klopp his first appearance at Wembley as the Liverpool manager three months after replacing Brendan Rodgers. Milner, who scored in the shootout, admits the change of manager has been difficult but believes Liverpool can lay the foundations for further success if, in a season of adaptation, they win silverware on 28 February.

“This club is built on success – they’re used to winning trophies,” said the Liverpool vice-captain. “It’s always tough changing managers. There has been a big change: in the playing staff and on the ground. We can win a trophy and be in the hunt for others during a transition season when it’s easy to say: ‘There’s been a lot of changes – let’s see how we do; do the best we can and go again next year.’

“Hopefully we can do both: the transition with the new manager and keep improving – get a few players back as well. The longer this team is together, with the signings that come in the summer, along with the manager and the coaching staff, the better we’ll get.”

Milner and Adam Lallana described Liverpool as poor in the first half against Stoke. Lallana said: “There were strong words at half-time. Not just from the manager but from ourselves. We knew it.” Milner said the team must improve but they should take encouragement from also being in the last 32 of the Europa League and, the midfielder believes, still in with a chance of Champions League qualification despite their search for consistency and injury problems.

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Milner said: “At times we haven’t performed with the quality we want – we know we can improve – but the bottom line is we’re still in every competition. We’re not a million miles off in the league. With a few more points and a few more goals, we’ll be closer [to the top four]. With a strong finish, we can be in a reasonable position. Saying that, we’re a long way from where we want to be. Considering the results we’ve ground out, we can be proud at this moment in time. There’s definitely a lot more to come from this squad.”

Reflecting on his time at Manchester City Milner added: “Winning the FA Cup gave us the belief that we could go and win trophies. The first one is always important, to have that winning habit; to get over the line. The first one gave us the belief to go and win the league the next year. We’re in a final and it’s one step further than we got last year. It’s pleasing. We’ve got a lot of improving to do as well. If we can do that, it should be exciting times at the club.”

Liverpool’s attentions have turned to Saturday’s FA Cup third round tie at home to West Ham United. Milner says Liverpool are keen to avenge home and away Premier League defeats by Slaven Bilic’s team this season.

“They have done us haven’t they?” he said. “Cup ties are always different but we do owe them one. It is important we recover over the next few days. There are a lot of tired boys in the dressing room who have given everything over the last few games and, with the emotion of the last two games, it is important we are not flat at the weekend. We need to ensure we are straight back on it again.”